In a way, Finnick has outsmarted Katniss here by saving Peeta's life. Now Katniss "will never stop owing Finnick." He's done her the kind of favor she can't easily pay back; now she can't let him down. Inside the arena, this kind of relationship will ultimately be a liability – nobody wants to have to kill her own friends.

Katniss constantly has to be thinking on her feet. She's always being watched, especially in the arena. Not only does she have to worry about the other players, she has to worry about the people who designed the game. The Quell isn't static; the people behind the scenes could easily tweak it to make it more difficult. So Katniss has to play dumb and try to retain her "valuable piece of information."